color glass condensate and the relation to hera …...ringberg workshop new trends in hera physics...

Ringberg Workshop New Trends in HERA Physics 2008, October 5-10, 2008, Ringberg Castle, Tegernsee CGC and the relation to HERA physics - p. 1

Color Glass Condensate and the relation toHERA physics

Edmond IancuIPhT Saclay & CNRS

Introduction

Motivation

Gluon evolution at small x

AdS/CFT

CGC & Geometric scaling

Some consequences for HERA

Backup


Introduction: What is CGC ?

■ The ultimate form of hadronic matter at high energy◆ “parton saturation” (maximal occupation numbers)

■ A firm prediction of first–principle calculations◆ weak coupling (perturbative QCD)◆ strong coupling (AdS/CFT for N = 4 SYM)

■ Interesting conceptual aspects◆ high energy limit of scattering amplitudes◆ multiple scattering, saturation, unitarity◆ relation to modern problems in statistical physics

■ Interesting consequences for the phenomenology◆ rapid growth of the gluon distribution (HERA)◆ geometric scaling (HERA)◆ particle production in pA and AA collisions (RHIC)

■ Decisive tests are coming soon, at LHC !

Introduction

Motivation


AdS/CFT



Backup


Motivation: Gluons at HERA

⊲ The gluon distribution rises very fast at small x ! (∼ 1/xλ)

H1

Col

labo

ratio

n

xG(x,Q2) ≈ # of gluons with transverse size ∆x⊥ ∼ 1/Q and kz = xP

Introduction

Motivation


AdS/CFT



Backup


Motivation: High density = Weak Coupling

H1

Col

labo

ratio

n⊲ High–energy evolution : An evolution towards increasing density.

⊲ High density partonic matter is weakly coupled !

Introduction

Motivation


AdS/CFT



Backup


Motivation: High density = Non-linear

⊲ A challenging problem though !

High density =⇒ weak coupling but strong non–linear effects

Introduction

Motivation


● Small-x evolution

● BFKL

● Saturation momentum

● Dipole frame

● BFKL equation

● Non–linear evolution


AdS/CFT



Backup



■ The ‘infrared sensitivity’ of bremsstrahlung favors the

emission of ‘soft’ (= small–x) gluons

dP ∝ αsdkz

kz= αs

dx

x≡ αs dY

Y ≡ ln1

x∼ ln s =⇒ dY =

dx

x: “rapidity”

■ A probability of O(αs) to emit one gluon per unit rapidity.

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup



■ In turn, the emitted gluon can radiate an even softer one

■ The ‘price’ of such an additional gluon:

P(1) ∝ αs

∫ 1

x

dx1

x1= αs ln

1

x= αsY

■ Ordering in x =⇒ Ordering in (life)time (“glass”) :

∆t ∝ kz

k2⊥

∝ x

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


BFKL evolution

■ The blowing–up gluon distribution

xG(x,Q2) ∝∑

n

1

n!

(

αs ln1

x

)n

∼ eωαsY

Y ≡ ln (1/x) ∼ ln s : “rapidity”

■ “BFKL resummation” (Balitsky, Fadin, Kuraev, Lipatov, 75–78)

■ Conceptual difficulties in the high energy limit

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


Onset of non–linear dynamics

■ The gluon occupation number (or ‘packing factor’) :

n(x, k⊥, b⊥) ≡ dN

dY d2k⊥d2b⊥∼ 1

Q2× xG(x,Q2)

πR2

■ n ∼ 〈AiAi〉 : when n ∼ 1/αs ⇐⇒ Aia ∼ 1/g

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


The Saturation Momentum

■ The gluons must be numerous enough (small x) and

large enough (low Q2) to strongly overlap with each other.

Q2s(x) ≃ αs

xG(x,Q2s)

πR2∼ 1

xλ

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


Dipole factorization for DIS

■ At small–x, the struck quark is typically radiated off

the gluon distribution in the proton

■ Lorentz boost to the ‘dipole frame’

γ∗ fluctuates into a qq pair which then scatters off the proton.

■ The proton still carries most of the total energy !

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


Dipole factorization for DIS

σγ∗p(x,Q2) =

∫ 1

0

dz

∫

d2r |Ψγ(z, r;Q2)|2 σdipole(x, r)

σdipole(x, r) = 2

∫

d2b T (x, r, b)

■ T ≡ 1 − S : The dipole–proton scattering amplitude

■ Unitarity bound: T ≤ 1 (T = 1 : ‘black disk limit’)

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


BFKL evolution: Unitarity violation

■ The ‘last’ gluon at small x can be emitted off any of the

‘fast’ gluons with x′ > x radiated in the previous steps :

∂n

∂Y≃ αsn =⇒ n(Y ) ∝ eωαsY

■ Dipole forward scattering amplitude: T ∼ αsn

■ Unitarity bound (T ≤ 1) is eventually violated by BFKL !

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


BFKL evolution: Infrared diffusion

■ The gluon emission vertex is non–local in transverse space:

∂Y n(ρ, Y ) = αsn + αs∂2ρn

=⇒ Diffusion in ρ ≡ ln k2⊥

∼ lnQ2

Y

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


Non–linear evolution: Saturation

■ High density: recombination processes leading to saturation

∂n

∂Y≃ αs∂

2ρn + αsn − α2

s n2 = 0 when n ∼ 1

αs≫ 1

■ Non–linear equation =⇒ stable fixed point at high energy !

■ Unitarity restoration & Hard momentum scale (Qs(Y ))

Introduction

Motivation



● BFKL


● Dipole frame

● BFKL equation



AdS/CFT



Backup


Non–linear evolution: Saturation

∂Y n(ρ, Y ) = αs∂2ρn + αsn − α2

sn2

■ Cartoon version of BK (Balitsky–Kovchegov) equation (99)

■ Mean field (large–Nc) approx. to JIMWLK equation (CGC)(Jalilian-Marian, E.I., McLerran, Weigert, Leonidov, and Kovner, 97–00)

■ Derived to leading–order in perturbative QCD

Introduction

Motivation


AdS/CFT

● Strong coupling

● Saturation line



Backup


DIS at strong coupling(Polchinki, Strassler, 02; Hatta, E.I., Mueller, 07) see talk by R. Peschanski

■ λ ≡ g2Nc ≫ 1 with g2 ≪ 1 =⇒ AdS/CFT correspondence

■ N = 4 SYM ⇐⇒ classical gravity in the AdS5 × S5

■ Parton branching at strong coupling :

No reason to favour special corners of phase–space !

■ All partons have branched down to small values of x !

Introduction

Motivation


AdS/CFT

● Strong coupling

● Saturation line



Backup


Saturation line: weak vs. strong coupling

■ No ‘leading–twist’ (no pdf’s !) at Q2 > Q2s(x)

all partons lie within the CGC with occupancy n ∼ O(1)

■ Saturation exponent : Q2s(x) ∝ 1/xλs ≡ eλsY

◆ weak coupling : λs ≈ 0.4 g2Nc (LO BFKL Pomeron)

◆ strong coupling : λs = 1 (graviton)

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC

● Saturation front

● Gluon distribution

● Traveling wave

● Geometric scaling

● Geometric scaling at HERA

● Qsat at NLO


Backup


The Color Glass Condensate(McLerran, Venugopalan, 1994; E.I., Leonidov, McLerran, 2000)

■ An effective theory for the evolution towards saturation

■ Small–x gluons: Classical color fields radiated by fast colorsources (x′ ≫ x) ‘frozen’ in some random configuration ρa

■ WY [ρ] : Probability distribution for the color charge density

■ Functional evolution equation for WY [ρ] : JIMWLK

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Deep Inelastic Scattering off the CGC

■ T (r)[ρ] : scattering off a given configuration ρ of the color

sources (multiple scattering in the eikonal approximation)

■ Average over ρ with weight function WY [ρ] (glass)

〈T (r)〉Y =

∫

D[ρ] WY [ρ] T (r)[ρ]

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Saturation momentum

■ Saturation front : T (ρ, Y ) with ρ = ln(1/r2)

=⇒ a front interpolating between T = 0 and T = 1

ρρ ρ

1/2

1

ss(Y )2)( Y1

T

2YY1> Y1

■ The position ρs(Y ) of the front =⇒ saturation momentum

BK =⇒ ρs(Y ) ≡ lnQ2s(Y ) ≈ λY with λ ≈ 4.88αs ∼ 1

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Gluon occupation number

■ A similar front holds for the ‘unintegrated gluon distribution’

xG(x,Q2) =

∫

d2b

∫ Q

dk k n(x, k)

Y = 15Y = 10Y = 5

log(k2/k20)

n(k

)

35302520151050-5-10

10

1

0.1

0.01

0.001

1e-04

1e-05

log(k2/k20)

kn(k

)

6050403020100-10

1000

100

10

1

0.1

0.01

■ The typical transverse momentum of the gluons is ∼ Qs(Y )

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


BK equation: The traveling wave

■ The shape of the front is not altered by the evolution

log(r20/r

2)

T

2520151050-5

1

0.8

0.6

0.4

0.2

0

T (ρ, Y ) ≃ T (ρ− ρs(Y )) ≡ T(r2Q2

s(Y ))

■ ‘Geometric scaling’E.I., Itakura, McLerran (02) ; Mueller, Triantafyllopoulos (02)

■ Traveling wave picture : Munier, Peschanski (03)

■ Relation to Stat Phys : ‘reaction–diffusion’ A ⇋ 2A

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Geometric scaling

ln Qln Λ

Y = ln 1/x

22QCD

ln Q (Y)2s

■ ρ− ρs(Y ) = const : A line of constant gluon occupancy

=⇒ physics must be invariant along any such a line !

■ Saturation makes itself felt in the dilute regime (Q2 > Q2s)

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Geometric scaling

■ Strictly true only within a finite ‘scaling window’ above Qs,

which extends with Y : lnQ2g(Y ) − lnQ2

s(Y ) ∝ √αsY

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Geometric Scaling at HERA(Stasto, Golec-Biernat and Kwiecinski, 2000)

σ(x,Q2) ≈ σ(τ) with τ ≡ Q2/Q2s(x), Q2

s(x) = (x0/x)λ GeV2 , λ ≃ 0.3

x ≤ 0.01

Q2 ≤ 450 GeV2

Q2s ∼ 1 GeV2

for x ∼ 10−4

10-1

1

10

10 2

10 3

10-3

10-2

10-1

1 10 102

103

E665

ZEUS+H1 high Q2 94-95H1 low Q2 95ZEUS BPC 95ZEUS BPT 97

x<0.01

all Q2

τ

σ totγ*

p [µ

b]

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Geometric Scaling at HERA (2)(Marquet and Schoeffel 2006)

10-2

10-1

1

β dσ

diffγ*

p /dβ

(µb

)

H1 data (LRG)

ZEUS data (Mx) *0.85

ZEUS data (LPS) *1.23

10-2

10-1

1

10-2

10-1

1

1 10 102

τd1 10 10

2

τd

10-1

1

10

1 10 102

ZEUS dataH1 data

τV

σ DV

CS (

nb)

1

10

10 2

10 102

ZEUS dataH1 data

τV

σ VM

(nb

)

1

10

10 2

1 10

ZEUS data

τV

σ VM

(nb

)1

10

10 2

10 102

ZEUS dataH1 data

τV

σ VM

(nb

)

Introduction

Motivation


AdS/CFT


● CGC

● DIS off the CGC



● Traveling wave



● Qsat at NLO


Backup


Saturation exponent at NLO

D.N. Triantafyllopoulos, 2002

5 10 15 20 25

0.2

0.4

0.6

0.8

1

a

b

c

d

e

All with running coupling

a. brownb. greenc. blued. magentae. black

: L BFKL with: L BFKL: L BFKL + boundary: L RG BFKL + boundary: NL RG BFKL + boundary

Y0 =0

λ(Y ) ≡ d lnQ2s(Y )

dY≈ 0.3

■ NLO BFKL + Collinear resummation + Saturation Boundary

Introduction

Motivation


AdS/CFT



● Saturation models

● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction

● Soft diffraction (?)

● Semi-Hard diffraction

Backup


The unreasonable effectiveness of the ‘saturation models’

■ “Saturation models” ≡ QCD–inspired models for σdipole

involving saturation and a reasonable # of free parameters

■ The parameters are fixed by fits to the F2 data alone !

■ Satisfactory description of the ensemble of HERA data atx ≤ 0.01

All other observables (FD2 , FL, F

c2 , ρ, J/ψ, DVCS, ...)

emerge as ‘predictions’.

■ Important qualitative predictions of the theory which appearto be consistent with the data.

geometric scaling, the transition towards low Q2 for F2,a nearly constant σdiff/σtot ratio ...

■ A similar success for the relevant data at RHIC

high–p⊥ suppression in forward d–Au collisions (‘RpA’)

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Saturation models

■ The Golec-Biernat and Wüsthoff model (1999)

σGBWdipole(x, r) = 2πR2

(

1 − e−r2Q2

s(x)

)

, Q2s(x) = (x0/x)

λ GeV2

◆ Good fit to the early HERA data with only 3 parameters

◆ Exact ‘geometric scaling’ built in : σGBW(r2Q2s(x))

■ More sophisticated models (pQCD evolution, geometricscaling violations)

◆ DGLAP–like (also with b dependence) Bartels, Golec-Biernat,Kowalski (02), Kowalski, Teaney (03), Kowalski, Motyka, Watt (06)

◆ CGC model (BK eq.) E.I., Itakura, Munier (03) : 3 light quarks

◆ Improvements of CGC model: heavy quarks,b–dependence Kowalski, Motyka, Watt (06), Soyez (07)

◆ FS04 saturation model Forshaw, Shaw (04)

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


A CGC fit to F2 (G. Soyez, 2007)

x ≤ 10−2 , Q2 ≤ 150 GeV2 (281 data points, ZEUS & H1)

10-6 10-5 10-4 10-3 10-2

x

10-1

1

101

F2

(x1.

5n )

0.045

0.065

0.085

0.11

0.15

0.2

0.25

0.3

0.4

0.5

0.65

Q2 (GeV2)

10-4 10-3 10-2

x

1

101

102

F2

(x1.

3n )2

2.5

3.5

56.58.51012152022252735456090120150Q2

4 parameters: R, x0 ≈ 2× 10−5, γ ≈ 0.26 and λ ≈ 0.22 (χ2 = 0.90)

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


A CGC fit to F2 (G. Soyez, 2007)

0.1

1

10

1e-07 1e-06 1e-05 0.0001 0.001 0.01

Q2 (

GeV

2 )

x

Qs2

limit of geometricscaling window

H1ZEUS

light+heavy (GS)light only (IIM)

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


A CGC fit to F c2

Forshaw, Sandapen and Shaw (06)

0

0.1

0.2

0.3

0.4

ZEUSm

c = 1.15

mc = 1.35

mc = 1.55

0

0.2

0.4

0.6

H1

0.0001 0.001 0.010

0.2

0.4

0.6

0.8

0.0001 0.001 0.01 0.0001 0.001 0.01

Q2 = 1.8, 2.0 Q

2 = 4.0 Q

2 = 7.0 Q

2 = 11.0

Q2 = 12.0 Q

2 = 18.0 Q

2 = 25.0 Q

2 = 30.0

F2

c

Q2 = 130.0Q

2 = 60.0Q

2 = 45.0

x

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Saturation fits for Diffraction

Forshaw, Sandapen and Shaw (06) Low Q2

0.02

0.04

0.06

ZEUS FPC FS04 sat b= 6.8 GeV-2

FS04 no sat b=8 GeV-2

CGC b=6.8 GeV-2

Q2 = 6 GeV2Q2 = 4 GeV2

=0.6522

Q2 = 2.7 GeV2

xIP

x IP FD

(3)

2

=0.0044 =0.0066

0.02

0.04

0.06

=0.2308

=0.0099 =0.0148

=0.032 =0.0472

0.02

0.04

0.06

=0.0218

=0.1429

0.02

0.04

0.06

=0.0067

=0.3077 =0.4

10-4 10-3 10-2

0.02

0.04

0.06

=0.003

10-4 10-3 10-2

=0.7353

10-4 10-3 10-2 10-1

=0.8065

0.02

0.04

0.06

=0.0698=0.1

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Saturation fits for Diffraction

Forshaw, Sandapen and Shaw (06) High Q2

0.02

0.04

0.06=0.0088

Q2 = 55 GeV2Q2 = 27 GeV2Q2 = 14 GeV2

Q2 = 8 GeV2x

IP

x IP FD

(3)

2

=0.0153=0.0291

0.02

0.04

0.06=0.0196

=0.0338 =0.0632

ZEUS FPC FS04 sat b = 6.8 GeV-2

FS04 no sat b = 8 GeV-2

CGC b = 6.8 GeV-2

=0.1209

0.02

0.04

0.06=0.062 =0.1037 =0.1824 =0.3125

0.02

0.04

0.06=0.1818 =0.28 =0.4286 =0.6044

0.02

0.04

0.06=0.4706 =0.6087 =0.75 =0.8594

10-4 10-3 10-2

0.02

0.04

0.06=0.8475

10-4 10-3 10-2

=0.9067

10-4 10-3 10-2

=0.9494

10-4 10-3 10-2 10-1

=0.9745

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Saturation vs. Regge fits for F2

Forshaw and Shaw (04) Relatively low Q2

10-6 10-5 10-4 10-3 10-2 10-1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

F 2

x

Q2=15 GeV2

Q2=0.25 GeV2

Q2=2.7 GeV2

10-6 10-5 10-4 10-3 10-2 10-1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

F 2

x

Q2=15 GeV2

Q2=0.25 GeV2

Q2=2.7 GeV2

■ Left: Regge fits (a sum of ‘soft’ + ‘hard’ Pomerons)

■ Right: 2 saturation fits (FS04 and CGC)

■ Data appear to prefer saturation !

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


DIS Diffraction

Ygap

Q2}

MX

rQ2 }

M2X∼ Q2

■ An ideal laboratory to study saturation/unitarity effects

◆ sensitive to relatively large dipole sizes

◆ sensitive to theoretical models (or prejudices)

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


DIS Diffraction

Ygap

Q2}

MX

rQ2 }

M2X∼ Q2

■ An ideal laboratory to study saturation/unitarity effects

◆ sensitive to relatively large dipole sizes

◆ sensitive to theoretical models (or prejudices)

■ Original prejudice: “Even for large Q2, diffraction is soft”

σdiff ∝ x−2(αP−1) and henceσdiff

σtot∼ x−(αP−1) at small x X�

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Diffractive over inclusive ratio at HERAGolec-Biernat, Wusthoff (99) ; Bartels, Golec-Biernat & Kowalski (02)

σdiff/σ

tot

ZEUSQ2 = 8 GeV2

Q2 = 14 GeV2Q2 = 27 GeV2

Q2 = 60 GeV2

Satur. Mod. with evol MX < 3 GeV

3 < MX < 7.5 GeV

W(GeV)

7.5 < MX < 15 GeV

0

0.02

0.04

0.06

0

0.02

0.04

0.06

0

0.02

0.04

0.06

40 60 80 100 120 140 160 180 200 220

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Diffractive dissociation of the virtual photon

dσdiff

d2b=

∫

dz d2r |Ψγ(z, r;Q)|2

(

T (r, Y ))2

■ The photon wavefunction favors small dipoles (r ∼ 1/Q)

dσdiff

d2b∼ 1

Q2

∞∫

1/Q2

dr2

r4

(

T (r, Y ))2

■ The dipole amplitude favors relatively large dipoles :

T (r) ∝ r2 (single scattering)

■ “The integral is dominated by large, non–perturbative,

dipoles with size r ∼ 1/ΛQCD, hence the soft pomeron ! ”

Introduction

Motivation


AdS/CFT




● GBW

● CGC fit to F2

● F2c

● F2D3

● F2D3

● F2 Regge vs Sat

● DIS Diffraction



Backup


Hardening the diffraction

■ At sufficiently high energy, gluon saturation cuts off the

large dipoles already on the ‘semi–hard’ scale 1/Qs !

dσdiff

d2b∼ 1

Q2

1/Q2

s∫

1/Q2

dr2

r4

(

r2Q2s(x)

)2

∼ Q2s(x)

Q2∝ x−λ

◆ σdiff is dominated by dipole sizes r ∼ 1/Qs(x) !

◆ σdiff ∝ x−λ : single, hard pomeron increase with 1/x

(instead of double soft !)

◆ σdiff/σtot ≈ constant ! X

■ ‘Semi–hard diffraction’ ... at intermediate energies !

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC

● Single scattering

● Multiple scattering

● No Jets


Stochastic aspects of high–energy QCD

■ Classical fields (JIMWLK) : no gluon–number fluctuations

■ Gluons in the same cascade are correlated with each other

■ Saturation & multiple scattering could probe the correlations

■ ‘Reaction–diffusion’ A ⇋ 2A Munier, Peschanski (03)

∂tn(x, t) = ∂2x n(x, t)

︸︷︷︸

diffusion

+ αn(x, t)︸︷︷︸

growth

−β n2(x, t)︸︷︷︸

recombination

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


DIS with Pomeron loops

■ Statistical physics: The effects of fluctuations are dramatic !(The front is pulled by the dynamics in its dilute tail)

■ Important consequences for high–energy QCD(Mueller, Shoshi; E.I., Mueller, Munier; E.I., D. Triantafyllopoulos, 2004)

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


Front diffusion through fluctuations

■ The stochastic evolution generates un ensemble of frontswhich differ by their saturation momentum ρs ≡ lnQ2

s

〈ρs(Y )〉 = λY, 〈ρ2s〉 − 〈ρs〉2 = DY, D ∼ 1

ln3(1/αs)

log(r20/r

2)

T

2520151050-5

1

0.8

0.6

0.4

0.2

0

■ With increasing energy, the fronts spread from each other

=⇒ geometric scaling is progressively washed out !

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


Dispersion: Fixed coupling

■ σ2(Y ) ≃ DαsY with D ∼ O(1)

0

5

10

15

20

25

0 10 20 30 40 50

σ2

Y

αs=0.2αs=0.5

■ Fluctuations effects are clearly important ...

αs = 0.5 =⇒ σ2(Y ) ≃ 10 for Y = 10

■ σ2(Y ) >∼ 1 =⇒ a totally new picture : ‘diffusive scaling’

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


Dispersion: Running coupling

■ The dispersion keeps rising with Y ...

0

1

2

3

4

5

0 10 20 30 40 50

σ2

Y

FC: αs=0.2FC: αs=0.5RC: β=0.72RC: β=0.50

■ ... but now it is tremendously smaller ! (by a factor ∼ 100)

■ No physical effect up to unrealistically large Y !

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


Single scattering: 2–gluon exchange

■ The dipole scatters off the gluon field in the target

V (r) ≃ gtar · Ea =⇒ T (x, r, b) ∝ g2r2〈Ea · Ea〉x

T (x, r, b) ≃ αs r2 xG(x, 1/r2)

πR2≡ αs n(x,Q2 ∼ 1/r2)

Weak scattering (T ≪ 1) ⇐⇒ Low gluon occupation (n≪ 1/αs)

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


Multiple scattering: Unitarization

■ When decreasing x at fixed r : xG(x, 1/r2) ∼ 1/xλ

=⇒ Unitarity is eventually violated ! (T >∼ 1)

■ Multiple scattering becomes important and restores unitarity

■ Eikonal approximation + Incoherent scattering =⇒

T (x, r) ≃ 1 − exp

{

−αs r2 xG(x, 1/r2)

πR2

}

(“Glauber–Mueller”)

Introduction

Motivation


AdS/CFT



Backup

● Fluctuations

● Pomeron loops

● Front diffusion

● Dispersion: FC

● Dispersion: RC



● No Jets


No forward jets !

■ No large–x partons =⇒ no forward/backward jets in a

hadron–hadron collision at strong coupling

t < 0

min

■ ‘The Nightmare of CMS’

|η| . ηmax(Q) = ln

√s

Q− ln

1

xs(Q), xs(Q) ∼ Λ2

Q2N2c

≪ 1

color glass condensate and the relation to hera …...ringberg workshop new trends in hera physics...

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